I assume since this is a sequence that only takes on postitive integer values, so that would mean is positive and therefore exponentiating would keep the inequality intact.

So

.

So yes, the sequence converges.

August 27th 2010, 08:23 PM

elim

not necessarily implies that it converges

August 27th 2010, 08:28 PM

Prove It

True, I misinterpreted the question, sorry. All I proved was that it was bounded.

According to Wolfram,

so yes, the sequence converges.

August 27th 2010, 09:29 PM

elim

Thanks a lot Sir!
what is the url at Wolfram?

August 28th 2010, 05:39 AM

chisigma

Is...

(1)

... and because ...

(2)

... is ...

(3)

Kind regards

August 29th 2010, 10:37 PM

elim

is not obvious. there are integer that make very close to hence is very big.

August 30th 2010, 02:33 AM

qspeechc

Do we have ?

August 30th 2010, 03:55 AM

Ackbeet

Reply to Elim at Post # 5:

Prove It is most likely referring to WolframAlpha. It's basically a way to enter single Mathematica commands. At least, that's what I use it for. Quite handy.

August 30th 2010, 06:33 AM

elim

Quote:

Originally Posted by qspeechc

Do we have ?

YES

August 30th 2010, 06:35 AM

elim

Quote:

Originally Posted by Ackbeet

Reply to Elim at Post # 5:

Prove It is most likely referring to WolframAlpha. It's basically a way to enter single Mathematica commands. At least, that's what I use it for. Quite handy.

Thanks a lot Ackbeet. Very nice to know the online tool.

August 30th 2010, 11:05 AM

chisigma

Quote:

Originally Posted by elim

is not obvious. there are integer that make very close to hence is very big.

The consideration of elim is quite correct. By definition say that...

(1)

... means that for any it exists an integer so that is...

(2)

Now if we measure angles in degree [for example] instead of in radians is and the sequence has no limit. If the angles are in radians then never vanishes and in my opinion the (1) is 'probably true', even if for 'very small' the (2) is satisfied for 'enormous' values of . In any case a rigorous prove has to be supplied and that is not a trivial job (Thinking)...

Kind regards

August 30th 2010, 12:17 PM

qspeechc

Quote:

Originally Posted by elim

YES

I don't mean to be irritating, but if you can show then we are done...

August 30th 2010, 01:23 PM

Defunkt

Quote:

Originally Posted by qspeechc

I don't mean to be irritating, but if you can show then we are done...